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Iterated Function Systems, Moments, and Transformations of Infinite Matrices

Palle E. T. JørgensenKeri A. KornelsonKaren L. Shuman

出版	American Mathematical Soc., 2011
主題	Mathematics / GeneralMathematics / CalculusMathematics / MatricesMathematics / TransformationsMathematics / Mathematical Analysis
ISBN	08218524859780821852484
URL	http://books.google.com.hk/books?id=vlPVAwAAQBAJ&hl=&source=gbs_api
EBook	SAMPLE

註釋

The authors study the moments of equilibrium measures for iterated function systems (IFSs) and draw connections to operator theory. Their main object of study is the infinite matrix which encodes all the moment data of a Borel measure on $\mathbb{R}^d$ or $\mathbb{C}$. To encode the salient features of a given IFS into precise moment data, they establish an interdependence between IFS equilibrium measures, the encoding of the sequence of moments of these measures into operators, and a new correspondence between the IFS moments and this family of operators in Hilbert space. For a given IFS, the authors' aim is to establish a functorial correspondence in such a way that the geometric transformations of the IFS turn into transformations of moment matrices, or rather transformations of the operators that are associated with them.